${10 \div \dfrac{5}{8} =}$
${10} \div \dfrac{5}{8}} ={\dfrac{10}{1}} \div \dfrac{5}{8}} $ $~~~~~~~{\gray{\text{Rewrite 10 as }\dfrac{10}{1}}}. $ $\phantom{10 \div \dfrac{2}{3}}} ={\dfrac{10}{1}} \times \dfrac{8}{5}}$ $ ~~~~~~{\gray{\text{Multiply by reciprocal of }\dfrac{5}{8}.}} $ $\phantom{10 \div \dfrac{2}{3}}} ={\dfrac{{10}\times8}}{1\timesD5}} $ $~~~~~~~{\gray{\text{Multiply. }}} $ $\phantom{8 \div \dfrac{2}{3}}} ={\dfrac{80}{5}} $ $~~~~~~~{\gray{\text{Simplify. }}} $ $\phantom{8 \div \dfrac{2}{3}}} =16 $ ${10 \div \dfrac{5}{8} =16}$